Peter Martins rehearses Megan Fairchild and Gonzalo Garcia in "La Sylphide" at the David H. Koch Theater, Lincoln Center. The 1836 ballet is new to the New York City Ballet. (Erin Baiano /For The Washington Post)

It’s Oscar season, even at the New York City Ballet.

“This is your moment,” Peter Martins says to Georgina Pazcoguin, an NYCB soloist. He’s trying to get her to gloat more. To demonstrate, he grabs a stick and thrusts it over his head as though he’s challenging the devil to a sword fight. His whole body shudders in exaggerated, vicious delight.

On a recent afternoon in the nearly empty, cavernous David H. Koch Theater at New York’s Lincoln Center, Martins, NYCB’s ballet master-in-chief, is leading a rehearsal of “La Sylphide.” In this 1836 ballet, a Scottish laird named James is rude to a witch, who in turn ruins his life and kills his sweetheart, the fairylike sylph of the title. Pazcoguin plays the witch, and Martins wants her to project her wicked joy at James’s suffering so that even those in the upper balconies can feel the sting.

“You have to be . . . ” Martins searches for a word. He shakes his fists in the air. “Boom!”

Old as it is, “La Sylphide” is new for NYCB. Martins originally staged this production for another company and brought it to NYCB last year. It’s part of his drive to challenge his dancers — and his audiences — with the unknown.

Tiler Peck in Justin Peck's "The Most Incredible Thing." (Paul Kolnik)

An organization as big as his, he said in a wide-ranging interview in his office, can take chances, push past boundaries. The two programs NYCB will perform at the Kennedy Center on March 1 to 6 exemplify that. One offers short contemporary works, including a ballet unveiled this month by resident choreographer Justin Peck, titled “The Most Incredible Thing.”

On the other program, separated by nearly 200 years, but in some ways as unfamiliar to this company as a world premiere, is “La Sylphide.”

This story of broken hearts and human frailties is the best-known work of August Bournonville, an important Danish choreographer of the Romantic era and one of the greatest dance storytellers. His works are lively, warmhearted and atmospheric. (“La Sylphide” moves from a Scottish manor to a witch’s cave and a highland moor.) They require not only acting and mime, but also a distinctive light, airy style, in which the dancers should bound into the air with no force.

The Danish-born Martins, 69, grew up with “La Sylphide.” He danced small parts while studying at the Royal Danish Ballet School, and he progressed to the role of James before leaving Copenhagen in 1970 to join NYCB.

“It fit perfectly,” he says of dancing Bournonville’s buoyant choreography. “Everything fits the music so well. It’s unforced and organic.” (Martins is linked to “La Sylphide” by more than ballet heritage; he’s distantly related to the composer of its enchanting score, Herman Severin Løvenskiold.)

But Martins’s dancers, who are schooled in George Balanchine’s athletic, streamlined style, have little experience with acting and almost none with mime — hence, Martins’ hands-on drama coaching.

With the mime, “less is more,” says Sterling Hyltin, a principal ballerina who is scheduled to dance the leading role in Washington. “You have to keep it simple. If there are too many flourishes, it’s too cluttered, and the audience can’t read what your saying.”

Indiana Woodward in "La Sylphide.” (Paul Kolnik)

What looks simple in the dancing, however, requires unusual effort. “I honestly would go home at night the first week feeling like I had the flu,” Hyltin says. Embodying that misty sylph demands “one of the most incredible amounts of strength of any role I’ve ever done.”

She can’t use her arms for liftoff when she jumps — and sylphs do a lot of jumping — because the arms must travel more slowly than the body, billowing a little as the dancer lands, for an illusion of weightlessness.

This all comes together in her first solo, just after the curtain rises, when the sylph shows us how light and supernatural she is, and how much in love, with a skimming, spinning dance. There’s one particularly tricky turn early on, which revolves to the left (most dancers prefer the right), on the ball of one foot, which makes it a little more awkward than whirling cleanly atop a friction-free full pointe.

“That’s not even in our vocabulary,” Hyltin says. “It comes all of a sudden, and it’s, like, ‘Omigosh, I’m here at the attitude turn, I’ve arrived!’ ”

Martins has overseen every aspect of “La Sylphide,” aiming to keep it as pure as he remembers it from his youth, while also making sure the mime makes sense for today’s balletgoers. It’s a rare look back at his roots, and at what set him apart as an especially regal dancer with a clean technique and affinity for the air. You see that still in his impeccable posture. Martins dominates the stage at the “Sylphide” rehearsal with the broad, open shoulders and upright bearing of a ballet kingdom’s prince, even in his work wear of jeans and a plaid shirt.

In contrast to “La Sylphide,” Peck’s ballet — and indeed the rest of NYCB’s repertoire — highlights what distinguishes the company from many other arts organizations. Its products are almost entirely homegrown.

“My favorite line,” Martins says, speaking with the pride of an automaker, “is ‘Made on the Premises.’”

Sitting on the sofa in his book-lined office, Martins notes that he and his Danish-born “La Sylphide” are the rare exceptions. Otherwise, the dancers and the dances and even most of the decor and costumes are still produced in-house. (Susan Tammany, who created the sets and costumes for “La Sylphide,” is a Koch Theater usher — strange as that may sound — as well as a painter. )

Unlike most ballet companies, NYCB never holds open auditions. Nearly all the dancers emerge from its official training arm, the School of American Ballet, just across the Lincoln Center plaza. And the ballets are created in the studios down the hall, by choreographers invited by Martins to make original works.

“We don’t borrow ballets; we don’t license ballets,” Martins says. “We don’t even co-commission. We are very selfish. We like to do everything ourselves.”

Insisting on works created in-house means being open to risk. Martins doesn’t know what he’s going to get when he commissions a piece. Human frailty, a theme cherished by Bournonville, is something he has to reckon with when he stakes a season on new choreography. But the risks are necessary. he says.

We talk about Peck’s “The Most Incredible Thing,” which harks to the Ballets Russes era: It’s a condensed narrative ballet, based on a Hans Christian Andersen fairy tale, made in collaboration with two young, successful artists. Indie rocker Bryce Dessner, who contributed to “The Revenant’s” soundtrack, composed the music. Brooklyn-based sculptor and painter Marcel Dzama made the sets and costumes. I'm eager to see it again; based on an initial viewing, I can say the music, costumes and decor are impressive, and although clarity isn’t always apparent in the choreography, the effect grows more powerful toward the end.

What especially struck me was the number of young people in the audience, which Martins says is the ripple effect of his Art Series initiative. In this annual project, NYCB commissions an artist to create original works to display at the Koch Theater. Dzama, inspired by chess fan Marcel Duchamp, made a surreal, chess-inspired installation for the theater’s promenade, including a metal mobile that’s like a merry-go-round of alien fertility totems, as well as sculptures of giant chess pieces. The company markets a few performances each season specifically to the artist’s followers, with lowered ticket prices. Art-loving newcomers with an enthusiasm for experimental work show up, and, according to NYCB, many tend to return.

The relative flushness is great, Martins says, but his investment in human capital, especially young choreographers, is an unshakable guiding philosophy.

“If you don’t try,” he says, “if you don’t offer people opportunities, you’ll never go anywhere. Do you believe in the future? Do you believe in new choreography? Then you must offer opportunities.”

Balanchine was the exemplar of that principle, he says. “How many choreographers did he invite in? It’s not known, because a lot of them were not very good and they disappeared after a while. But that didn’t stop him from inviting them. He never stopped trying.”

When Martins was in his 30s and had begun making ballets, Balanchine took him to lunch. “He said, ‘You know, dear, if you do one good ballet out of 10 that is a really good ratio.’ Really? I said. And he said, ‘Look at me. How many ballets have I done? More than 400. And how many do we dance now? Maybe 70. Look at the ratio. And I was better than anybody else!’ ”

Martins laughs. “So if you have one out of 10, you’re very good. But there are no shortcuts. You have to do the other nine!”

Patience is key, Martins says. But so is pushing an artist into new territory, where he might well fail, but he’ll do so while experimenting, and that is the best way to grow.

He counts off the choreographers whose careers blossomed at NYCB: Alexei Ratmansky, Christopher Wheeldon, Benjamin Millepied, in addition to Peck. “They get invited around the world to create ballets for other companies. Why? Because they were successful here. And those other companies also want the success. So what does a young choreographer do?”

They go back to the pattern that produced their original success, he says. And that becomes a trap: “You don’t necessarily grow. You repeat. Kiss of death.”

Certainly, a choreographer can dip back into his formula once in a while. But, Martins says, “what I want is growth. I don’t want you to repeat a ballet you’ve always done. Would I like a success? You bet.  But I’m not looking for a success. I’m looking for growth. Pick a different composer. Learn. Don’t fall into a groove. Take some chances. That’s the only way you’ll maybe accomplish the one out of 10.”

The works forming the centerpieces of the Washington programs carry a hefty price tag: “La Sylphide” cost about $1.4 million, and “The Most Incredible Thing” came to about $1.3 million. (Both were largely covered by donors to NYCB’s New Combinations Fund for new work.)

It helps that the company is on solid financial footing, having emerged from some dark years. According to a company official, in 2010, NYCB’s deficit reached a high of $8.5 million. That deficit was eliminated in three years, and the company has boasted a modest surplus since 2013. It has an endowment of $181 million.

But taking artistic misfires in stride is part of the company’s DNA, Martins says. When he created a flop, he says, he remembers Balanchine saying to him, “‘Bad ballet — not the end of the world. It’s just a little ballet.’”

If a new piece doesn’t go over terribly well, Martins offers choreographers the chance “to revisit, look at it again, play with it. You may decide to throw it away and do another one. Or you decide next season to fix a little bit.

“With this infrastructure here, we have the resources, we have the dancers. We all know there are no guarantees. However, we welcome the whole choreographic process of the unknown.”